CS 598: Spectral Graph Theory: Lecture 3 - Corelab
CS 598: Spectral Graph Theory: Lecture 3 - Corelab
CS 598: Spectral Graph Theory: Lecture 3 - Corelab
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Laplacian: The Perron-Frobenius<br />
Theorem<br />
• <strong>Theory</strong> can also be applied to Laplacians and any<br />
matrix with non-positive off-diagonal entries. It<br />
involves the eigenvector with smallest eigenvalue.<br />
Perron-Frobenius for Laplacians:Let M be a matrix<br />
with non-positive off-diagonal entries s.t. the graph<br />
of the no-zero off-diagonal entries is connected.<br />
Then the smallest eigenvalue has multiplicity 1 and<br />
the corresponding eigenvector is strictly positive.<br />
Proof on blackboard.
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